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Number of compositions of n with exactly six occurrences of the largest part.
2

%I #7 Feb 10 2015 04:00:48

%S 1,0,0,0,0,0,1,7,28,84,210,462,925,1723,3038,5145,8498,13930,23143,

%T 39859,72500,140266,286678,609217,1323197,2897511,6339636,13787488,

%U 29726648,63472185,134190162,280988786,583076160,1199816068,2449963412,4967798570,10009806563

%N Number of compositions of n with exactly six occurrences of the largest part.

%H Joerg Arndt and Alois P. Heinz, <a href="/A243741/b243741.txt">Table of n, a(n) for n = 6..650</a>

%p b:= proc(n, p, i) option remember; `if`(n=0, p!,

%p `if`(i<1, 0, add(b(n-i*j, p+j, i-1)/j!, j=0..n/i)))

%p end:

%p a:= proc(n) local k; k:=6;

%p add(b(n-i*k, k, i-1)/k!, i=1..n/k)

%p end:

%p seq(a(n), n=6..50);

%t b[n_, p_, i_] := b[n, p, i] = If[n == 0, p!, If[i<1, 0, Sum[b[n-i*j, p+j, i-1]/j!, {j, 0, n/i}]]]; a[n_] := (k=6; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 6, 40}] (* _Jean-François Alcover_, Feb 10 2015, after Maple *)

%Y Column k=6 of A238341.

%K nonn

%O 6,8

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 09 2014